I love connecting to animals with my hands, especially horses. I own 3 horses, and I have an active hands on equine massage/healing practice in the Phoenix area. (equinebodyfreedom.com) Healing with your hands is really pretty easy. Start at the shoulders, or withers on a horse, and place your hand lightly on the animal's fur, holding it there with connection and lightness, as though you were feeling for something. It should be a comforting touch, like you are holding a dear friend's hand softly yours. Allow your hand to feel the animal's energy. Receive first. Try to understand what you are feeling by asking your body to interpret the feeling. Just gather information, and watch the animal. Their eyes may change, maybe blinking, or fluttering. They may yawn. A horse will probably stand quietly, but a dog or cat may start to squirm a little because the energy they are experiencing may be odd to them at first. You can always lighten up. Try not to pet or rub. Just stay steady.
Once you feel the animal's energy in your hand, change your intention to mirroring that energy back to them, filled with love. You are standing witness to them, mixing your loving energy with theirs and sending it back to them at their level, so that they can absorb it best. Once you have this feel, more your hand to a new spot. You can try moving along the bladder meridian- right below the top of the neck and the spine all along the animal from head to tail. Just take it slow, and let your hand rest and connect in each new position.

By paying attention to what you feel in your hand, and by observing the animal's eyes and expressions you will learn a lot about what they need. The animal will be more responsive in the places where their facia is restricted. Stay in the places a little longer. Sometimes there is something going on in that place - a sore muscle or a restricted joint - and sometimes there is just a fascial constriction there that may be coming from somewhere else in the body. So be careful "diagnosing", as the body is fully connected and mysterious. Just let your healing work do the job, and trust that you are magic!